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Unformatted text preview: load, and model the vector f as a random variable with known mean
E f = f (0) , E(f − f (0) )(f − f (0) )T = Σ.
In this case we would be interested in minimizing the expected stored energy, i.e.,
minimize E E (x, f (i) )
subject to l ≤ xi ≤ u, i = 1, . . . , m
Wtot (x) W.
Hint. If v is a random vector with zero mean and covariance Σ, then E v T Av = E tr Avv T =
tr A E vv T = tr AΣ.
(c) Formulate the four problems in (b) as semideﬁnite programming problems.
14.4 A structural optimization problem.  The ﬁgure shows a two-bar truss with height 2h and width
w. The two bars are cylindrical tubes with inner radius r and outer radius R. We are interested
in determining the values of r, R, w, and h that minimize the weight of the truss subject to a
number of constraints. The structure should be strong enough for two loading scenarios. In the
ﬁrst scenario a vertical force F1 is applied to the node; in the second scenario the force is horizontal
with magnitude F2 . h...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.
- Fall '13
- The Aeneid